Can blender export 2D curves to svg?
You can try Liero's addon Viewport to SVG: 


Download, install and enable add-on. 
Add-on appears in properties panel of 3D View window (N).
Setup output directory
Check Bezier Overlay option
Select curve objects you want to export and hit "Export SVG"


The final shape is determined by point of view (perspective/orthogonal). 
Addon exports all selected curve objects (3D curves as well).



Note: Bezier curve is exported with strange looking poly line version.
In Inkscape - click on this path and delete. In Illustrator – first Ungroup once (Cmd/Ctrl + Shift + G), than select and delete.



There is another add-on called Export SVG Format, which exports only active object. Shape of curve is determined by "Local Z" axis in Orthogonal view.
Addon is a bit messed up with naming – downloaded script is called "exporter.py", in blender's user preferences appears as "Export SVG Format" and in blender's File menu under Export you will find it as "Inkscape SVG".



Both addons exports only paths (no fills).